Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D268 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #431×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #431 | D67 |
| hypocenter | C67 | #3211 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #431 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16863930 | C2 | semidirect |
| 2. C2×#14524031 | C2 | semidirect |
| 3. #16863780 | C2 | semidirect |
| 4. #16863751 | C2 | semidirect |
| 5. #16863619 | C2 | semidirect |
| 6. #16863612 | C2 | semidirect |
| 7. #16863554 | C2 | semidirect |
| 8. #16863549 | C2 | semidirect |
| 9. #16863537 | C2 | semidirect |
| 11. #431×C67 | C2 | semidirect |
| 14. C2×Dic268 | C22 | semidirect |
| 16. C2×#11761617 | C22 | semidirect |
| 19. #14524035 | C22 | semidirect |
| 24. #14524031 | C22 | semidirect |
| 28. C4×Dic134 | C22 | semidirect |
| 29. C4×D268 | C22 | semidirect |
| 34. #14523968 | C22 | semidirect |
| 35. #14523968 | C22 | semidirect |
| 39. C4⋊C8×C67 | C22 | semidirect |
| 42. C4×C8×C67 | C22 | semidirect |
| 144. C67 | #3211 | semidirect |
| 155. #431 | D67 | semidirect |
| 179. C4⋊C8 | C2×D67 | semidirect |
| 186. C4×C8 | C2×D67 | semidirect |